Windows 10 doesn't require a key per se if you upgraded from Windows 8.1 to 10 then during the installation Windows would have given you a digitial activation automatically.
That can be verified by clicking
Start > Settings > Update & security > in left pane click Activation
You ought to see this:
Just beneath you see also the Product Key is a digital entitlement too.
This entitlement is assigned to your computer hardware. If you have changed any significant hardware such as motherboard for example this can void the digital entitlement as Microsoft database will think your computer is a different one. In that scenario you need to contact Microsoft, explain the situation so they can update their server database and reassigned your digital entitlement.
You can do that using the
Contact Support app
Click
Start > All apps > Contact Support where you can contact Microsoft several ways, set up a time to talk to them later, or literally speak to someone live then and there (there may be a few minutes wait for next available person though and it will tell you how long that wait is).
If your Activation splash screen says its activated then the alert you are getting could be malware on your computer in which case doing a thorough scan of your computer with security software would be wise.
Regarding the specific error message though. If it is legitimate then Microsoft published this page to explain the error and how to sort it:
https://support.microsoft.com/en-us/kb/3166553
